Category Archives: Musings & News

Fibonacci

Musings & News, Plants & Fungi

In the 13th century an Italian named Fibonacci changed the course of history. In the process he used numbers to describe this spiral. Here’s how.

Fibonacci was a great mathematician in the Middle Ages.  In 1202 he published Liber Abaci (Book of Calculation) to introduce the Arabic numeral system to Europe.

Until that time, Europe used Roman numerals for commercial bookkeeping.  Imagine CCXLVIII + MDCCCLXXIX = what?   The new math was adopted quickly because it boosted European commerce.

In his book, Fibonacci included lots of examples showing how to calculate using 0-9 digits with place value.   He also included “story problems.”  Here’s the rabbit problem:

If you start with 1 pair of rabbits, how many pairs will there be at the end of one year?

  • Start with 1 male and 1 female rabbit in a field
  • They produce 1 male and 1 female rabbit every month from their second month of age onward.
  • The young rabbits mature, pair up, and mate producing 1 male and 1 female per month from the second month of age onward.
  • The rabbits never die.

The answer is a mathematical pattern.   Start with 0 and 1 and put them in a row.  Add them together to produce the next number in the sequence.  Put this number at the end of the row and add those last two numbers to get the next one.  Keep doing this forever.

       0,1
0+1=1  0,1,1
1+1=2  0,1,1,2
1+2=3  0,1,1,2,3
2+3=5  0,1,1,2,3,5
3+5=8  0,1,1,2,3,5,8

The Fibonacci sequence is:  0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610,…

These numbers also describe spirals.

Imagine drawing squares whose edge lengths are the units in the Fibonacci sequence.  Each time you draw a new square, make it touch the ones you drew before.  Because each number in the sequence is larger, the new squares touch the old ones on their long edge.  Eventually you’ll notice that you are drawing squares in a spiral.  …Yes, this is hard to imagine. Here are some real life examples and Vi Hart’s YouTube video that shows how it works.

I’ve only grazed the surface of Fibonacci in nature so if you’d like to learn more see this educational math website from Surry, UK that has good, simple examples and animations.

I hope I haven’t lost you in math!  I get excited by these things.

(photo of a maypops tendril by Chuck Tague)

p.s. In August 2011, Science Friday reviewed a new book about Fibonacci.

Cool Water

Musings & News, Plants & Fungi


Here’s a place that’s changed for the better in the last 200 years.

Hells Hollow Falls are part of the gorge cut by Hell Run, a tributary of Slippery Rock Creek in Lawrence County. 

At its headwaters Hell Run flows through farmland, then into the woods where the gorge and waterfall have been protected as part of McConnell’s Mill State Park.

It wasn’t always this beautiful.

In the mid-1800’s the valley was logged and mined for its iron-ore-rich limestone and the coal to fire its industry.  The Lawrence Iron Furnace, two coal mines, a quarry, and a lime kiln were all within a short walk of the waterfall.  It must have been a smoky, dirty place in those days.

In the 1870’s the local iron business collapsed and within 50 years the coal mines closed too.  The trees grew back, the buildings disappeared, and the brick-walled lime kiln became a curiosity in the woods. 

The only noticeable scar is coal mining’s affect on the water.  The abandoned mines release toxic, orange, acid mine drainage (AMD) into Hell Run’s feeder streams above the falls.  Fortunately, even in the dry month of July there’s enough fresh water to dilute it. 

When I visited Hells Hollow Falls last Sunday I marveled at the miniature slot canyon upstream.  Geologists say this channel was formed when the creek ran inside a limestone cave just below ground level.  Eventually the top of the cave fell in and revealed the flume, pictured below.  If I was the size of an ant, this would be the Grand Canyon.

If you’d like to see these wonders for yourself, click these links for information on Hells Hollow and McConnell’s Mill State Park.

The waterfall looks cool … especially in this heat.

(photos by Kate St. John, taken on 17 July 2011)

Theories

Musings & News, Peregrines

One incident is unfortunate.  Two is a pattern. 

After one young peregrine died on Monday in this hall of mirrors and a second was injured yesterday, my brain has been working overtime trying to make sense of it all. 

Why were there no peregrine deaths in Oakland during the first five years of nesting but at least one per year since then?   What caused this?  What changed?

From the start of Pitt peregrine nesting in 2002 through the spring of 2007, only one youngster had an accident in Oakland and it didn’t kill him.  Crash hit a window on the Cathedral of Learning, fell into an architectural nook where he was trapped overnight, and was found in the street the next evening with a broken collar bone.  He went to rehab and was released successfully the following February.  (He actually released himself.)

Since 2008 the news has been bad.  Every year at least one juvenile peregrine has died near Fifth Avenue and Craig Street.  In 2008 Sky hit the windows of the Rand Building.  In 2009 a juvenile died in the Webster Hall chimney but wasn’t discovered until October.  In 2010 one juvenile died and another was injured in that same chimney (which was covered immediately).  This year Yellow Girl died and Red was injured hitting the Software Engineering Institute’s windows on Henry Street. 

What is going on?  Why do the juveniles spend time where it’s so deadly? 

My friend Karen Lang has an answer. 

In the spring and summer of 2007 the University of Pittsburgh cleaned the Cathedral of Learning.  Up to that point the building was a pigeon palace with nests in every nook and cranny.  At the end of the cleaning project the building was pigeon-proofed with netting to cover the access points.  With few pigeons at home our juvenile peregrines learn to hunt at the next nearest flock which happens to be at Fifth & Craig.  That area is a much more dangerous zone than the Cathedral of Learning because of its now-covered chimney and two mirror-glass buildings.  

Slowly, we humans are figuring this out.  The chimney was easy to fix.  The windows are harder.  

It would help if the pigeon flock moved to a safer location.

(photo of the Software Engineering Institute hall of mirrors on Henry Street by Kate St. John)

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Update on Red’s condition:  This morning I saw “Red” eating breakfast on Heinz Chapel steeple while both of his parents watched him.  Like all parents they could tell he wasn’t well and needed some extra attention.  Over at St. Paul’s Cathedral steeple, one of his remaining sisters whined.  She seems fine.  I hope she stays away from those windows!

Not To Worry

Musings & News, Schenley Park

Last week the Pittsburgh Tribune-Review reported that Phipps Conservatory is working through the approval process to install a modern 40-foot vertical-axis wind turbine at their upcoming Center for Sustainable Landscapes.

Since then Tony Bledsoe and I have received inquiries from folks who are worried that this windmill will hurt local birds, especially the peregrines, so I thought I’d discuss it today.  Please keep in mind that these are truly comments, not a news story.  I don’t know anything more than the media reported last week but I do know something about Schenley Park, birds, windmills, and our peregrines.

I’ll address the issues point by point:

  • Approval process:  Phipps is going through an approval process not because the windmill is dangerous but because Phipps Conservatory and Schenley Park are historic landmarks.  The wind turbine needs zoning approval because it’s 40 feet tall (four stories) in a historic setting.
  • It “looks more like a revolving door than a windmill”:   Though I don’t know what model is planned for Phipps, chances are it will look similar to the one pictured here in Rogiet, Wales.  It’s a spinning cylinder less than 10 feet wide.  Click here to see what this model looks like when the wind blows.
  • Will this windmill be a danger to birds?  Not likely.  The danger to birds depends on the location where the windmills are installed, the models used, and the number of windmills at the wind farm.  Altamont Pass Wind Farm, home of the famous killing-windmills, is one of the earliest, largest U.S. wind farms.  It houses nearly 5,000 small windmills on fretwork towers in ground-squirrel (prey) habitat in a migration corridor.  (See what it looks like here.)  The location attracts raptors who perch on the struts to hunt ground squirrels and die when they fly off the towers to capture prey.  Altamont has taught the wind energy industry what not to do.  To drive home that message Audubon won a lawsuit against Altamont’s owners, forcing them to replace the deadliest windmills.  Just to emphasize:  There’s a world of difference between a single 10-ft-wide revolving-door wind turbine in a city setting and 5,000 spinning-blade windmills in California’s migratory raptor habitat.
  • Will it hurt our peregrines?  Nope.  I’m not worried by it at all.  Peregrines are masters at avoiding moving things including waving flags and Life Flight helicopters (which you hear frequently on the Cathedral falconcam).  It’s what they don’t see that kills them.  Windows, not windmills, are the biggest killer of birds.  Birds see the sky’s reflections on windows, not the windows as walls, so they try to fly through them.  Up to 2.7 million birds per day are killed by windows in the U.S.   In 2008 one of Pitt’s young peregrines died by smashing into a window.   If you want to save birds, make windows safe.  Click here to read more from New York City Audubon.

Meanwhile, if you want to see a vertical-axis wind turbine I hear there’s one at the Eat’N’Park at Waterworks Mall near Fox Chapel.  Sounds like a good idea for a field trip:  sightseeing, shopping and eating.

(photo of a vertical axis wind turbine at Rogiet primary school in Wales by Andy Dingley.  Click on the photo to see the original on Wikimedia Commons.)

We Miss Her Already

Musings & News


Yesterday afternoon, Esther Gatewood Allen, naturalist, teacher, gardener and photographer passed away after suffering a stroke on June 13.

She took with her 93 years of experience outdoors, her great love of nature, her irrepressible curiosity and enthusiasm for plants, and her generosity in passing along her knowledge to everyone.

Active to the last, Esther had a “Keep going, Don’t stop” attitude that inspired everyone who knew her.  Perhaps she inherited it.  She grew up on a farm in Gallia County, Ohio, one of 11 children of Emma Rowena Gatewood who in 1955 at age 67 became famous as Grandma Gatewood, the first woman to thru-hike the Appalachian Trail alone.  By 1963 her mother had hiked the AT three times, the first person ever to do so.

Esther’s don’t-stop attitude gained her some fame including an interview with the Allegheny Front’s Justin Hopper and a chestnut tree planting on her 92nd birthday.  And she kept hiking too, though her goal was nature not mileage. Here she is chatting with George Bercik on an outing last summer.

Esther loved to teach.  I first met her in 1994 when I took her wildflower class at the Rachel Carson Institute.  I continued to learn from her by joining the Wissahickon Nature Club which she helped found in 1942 and where she taught at every meeting through her exhibits (pictured at top).

Esther knew everything about native plants — everything!  She was especially active in the Botanical Society of Western Pennsylvania whose members knew her better than I did.  Her home garden, which she tended by “letting it go,” was a joy and treasure trove to her fellow botanists.  If you needed to examine an unusual flower, chances are Esther could show it to you in her garden.  And any time we were stumped by a plant on an outing the cry went out, “Ask Esther!”

In the days before digital photography Esther took beautiful photographs which she used as slides while teaching and contributed as illustrations for the Botanical Society’s Wildflowers of Pennsylvania.  As in all things, Esther passed on this knowledge too.  Her photographic legacy is on this blog in beautiful photos by Dianne Machesney.

Esther leaves behind not only her family but a host of men and women she inspired with her enthusiasm for nature in western Pennsylvania.  We are Esther’s living, breathing legacy — people who love nature and want to pass it on.

I hope we can live up to her example.

We miss her already.

(Esther Allen teaching at a Wissahickon meeting, photo by Chuck Tague.  Esther chatting with George Bercik on a Wissahickon outing, June 2010, photo by Monica Miller)

Hearing Birdsong

Musings & News, Songbirds


Spring is here and the birds are singing.  It’s time to get our ears in tune to identify birds by song.

Did you know that even with excellent hearing there are some bird sounds we cannot hear?

Our ears are tuned to the sounds important to humans — our own voices, babies crying, the noises of danger — but our sense of hearing doesn’t pick up everything.

Animals are the same way.  Some birds make noises higher in scale than we can hear but it’s well within their own hearing range.  Golden-crowned kinglets and Blackburnian warblers are famous for singing high-pitched songs that sound fainter as they rise in pitch.  Some people can’t hear the high notes at all.

On the opposite end of the spectrum, whales sing below our range though sometimes we can feel their sounds as vibrations when they’re loud enough.

So what is our normal hearing range?  It’s different from person to person and the range narrows as we age.  Young people hear the widest spectrum.  Older adults lose hearing at the top of their range.

You can experiment with what you’re able to hear at this University of Kentucky Engineering webpage.  Read the instructions, then scroll down for a selection of recordings of different tones.  Each recording repeats the tone at a particular Hz level.  The recordings start loudly and become softer as they continue.

I discovered that my hearing range is 100 Hz up to 9000 Hz but at the far ends of the spectrum (100 and 9,000) I can only hear the tone when it’s very loud.  It disappears as it gets softer.

That may explain why I think golden-crowned kinglets sound fainter as they rise in pitch.  I’ll bet they’re singing with the same loudness the whole time but as they rise in pitch they approach the upper end of my hearing range.

The strangest part of the hearing test was when I clicked on the 60Hz and 10,000Hz recordings and heard nothing!   Those sounds are out there but I’ll never know.(*)

Try it yourself.

(photo of a Marsh Wren singing, by Chuck Tague)

(*) p.s. See the comments for information on the quality of sound from computer speakers vs. headphones.

UPDATE Nov 28, 2012: I tried this test again with better computer speakers and discovered I can hear 12,000 Hz, but it is so high that apart from the hearing test I would mistake it for ringing in my ears and not a noise produced in the wild.

UPDATE Dec 11, 2019: I tried the test again. I no longer hear anything at or above 8,000 Hz. 🙁

Animal, Vegetable

Musings & News
Emmy planning her attack on The Turnip, 19 March 2011 (photo by Kate St. John)

I usually write about wild things but this is a story about domesticated nature:  an animal and a vegetable.

This winter Esther Allen gave the members of the Wissahickon Nature Club an assignment.  Each of us must plant seeds from the kitchen and bring the results to the April 14th meeting.

My attempt with tangerine seeds failed to germinate and now, with less than a month left, I am running out of time so I bought a small turnip at the grocery store to sprout in water.  It shouldn’t take long.

I don’t like turnips — never buy them — so this one was a novelty.  About the size of a small red potato, it’s white and lavender with a tiny tap root and emerging leaves on top.  At some point I showed it to my cat.  Her reaction was surprising.

Emmy sniffed it, put her ears back, narrowed her eyes and gave it a sharp whack with her paw.  I tried hard not to laugh.  I hid my face in my book so she wouldn’t stop her assault on the turnip but I needn’t have worried. There was no stopping her.  She kept beating the turnip until she knocked it to the floor where it rolled like an ungainly mouse.  She attacked it from below, then charged at it, chased it back and forth, and nearly launched it down the basement stairs.

I rescued the turnip and hid it under a plastic bag on the kitchen counter but before I set it down I sniffed it myself.  As far as I could tell, it didn’t smell.

The next morning I sat drinking my coffee and Emmy puttered around the kitchen floor when suddenly her ears went back, she narrowed her eyes and sniffed the air.  Sniffing, sniffing, she moved below the spot on the kitchen counter where I had accidentally uncovered the turnip.   She’s not allowed on the counter (ha!) but she jumped right up to the turnip.

I had forgotten about it but she had not.  Apparently the turnip has a strong scent and she doesn’t like it, not one bit!

Emmy about to surprise-attack the turnip (photo by Kate St. John)
Emmy subdues the turnip (photo by Kate St. John)

How am I going to sprout the turnip with an attack cat in the house?

Maybe my excuse will be that the cat killed my homework.

Emmy whacks the turnip and sends it rolling (photo by Kate St. John)

p.s. Emmy is also called Emmalina.

(photos by Kate St. John)

Painted

Beyond Bounds, Musings & News


Everyone knows I love wild birds so I often receive gifts with birds drawn or sculpted on them.  Inevitably I try to identify the bird the artist used as a model.

Most products are made overseas nowadays, so the models could be real Chinese birds or inaccurately drawn from photographs of North American or European species.  I rarely assume they are totally fictional.

However, if I’d never seen a male painted bunting I’d think the artists invented this bird.

Definitely painted!

Chuck Tague photographed this one at a feeder at Merritt Island, Florida.

(photo by Chuck Tague)

Death By a Thousand Cuts

Musings & News

16 December 2010

For the past 100 years Pennsylvania has been great habitat for forest-nesting birds.  We’ve provided the nursery for 17% of the world’s scarlet tanagers and critical breeding grounds for wood thrushes and black-throated blue warblers.

But this is changing.  Right now.

Pennsylvania is at the beginning of the Marcellus Shale gas boom which will last for 30 years.  Now there are less than 3,000 wells.  If the boom goes as planned there will be 30,000 to 60,000 more.

Each well pad is a five acre industrial site connected by pipelines, compressor stations and roads.  This Google map shows what it looks like near West Union in Greene County (map is current).

From above you can see that the forest is fragmented by empty dirt squares and roads.  The scarlet tanagers that used to nest here are in Peru right now.  When they return they’ll find their nesting sites are gone or compromised.  There will be fewer nests and fewer scarlet tanagers born in Greene County next summer.  This is death by a thousand cuts.

Fragmentation isn’t new in Pennsylvania.  We’ve been doing it for farming, residential and commercial purposes for a very long time.  What’s new about this boom is that the fragmentation is industrial and is no longer around the forest edges or in farmland.  The Marcellus boom is going to the very heart of our prime forest habitat because the State Legislature has ordered DCNR to lease the state forests for gas drilling.

What does a drilled forest look like?  Below is a satellite image of the forest near Snow Shoe in Centre County. All those lines and patches are gas drilling sites. 

Sadly this fragmentation will last longer than it needs to because Pennsylvania has no money to restore the habitat when the drillers are gone.  We could have had that money but our state leaders, especially our Governor-elect (Tom Corbett in 2010) and the State Senate, oppose a Marcellus severance tax that would pay for habitat restoration and remediate a host of other problems caused by the gas boom.

What will happen to our forest birds?  It doesn’t look good, especially for black-throated blue warblers.  Read more here in Audubon Magazine and this extensive report by The Nature Conservancy on the effects of wind and gas energy development (the Marcellus summary is on page 30).

Will Pennsylvania change course?  Only if we work to make that change.

As Margaret Mead said, “Never doubt that a small group of thoughtful, committed citizens can change the world; indeed, it’s the only thing that ever has.”

(satellite images from Google Maps of the land in Greene and Centre counties, Pennsylvania)

p.s. There are many Marcellus shale issues and many groups working on them.  See fractracker.org’s Resources page for a list of groups.  Check out Fractracker’s main page for information on Marcellus Shale drilling.

A Crow in Jay’s Clothing?

Beyond Bounds, Crows & Ravens, Musings & News


To those of us in eastern North America this bird looks all mixed up.

He has a crow head, blue jay colors and an incredibly long tail.  He resembles crows and jays because he’s a corvid.  We don’t see him in Pennsylvania because he lives west of Iowa and east of the Sierra Nevadas.  Say hello to the black-billed magpie.

I saw this bird once, but now my sighting doesn’t count.  Years ago I saw a magpie outside my airplane window as we taxied to the gate at Charles de Gaulle airport in Paris.  Then, in their never-ending quest to reclassify birds the American Ornithological Union split the black-billed magpie from the European magpie and this bird dropped off my life list.   He is now Pica hudsonia.  The bird I saw in Paris was a Pica pica.

If I visited open country in the western U.S. I could easily re-add this bird to my list.  Black-billed magpies are loud and conspicuous, midway in size between blue jays and American crows.  Like crows they are smart, omnivorous and versatile.  Their claim to fame is their very long tail (more than half their body length) and their huge ball-shaped stick nests.

Maybe I should fly to Denver and look out the airplane window.  😉

(photo by Julie Brown)